Using Internet resources, find answers to questions:
Exercise 1
1. What is the information transfer process?
Transfer of information- the physical process by which information is transferred in space. They recorded the information on a disk and transferred it to another room. This process characterized by the presence of the following components:
2. General scheme transmission of information
3. List the communication channels you know
According to the type of distribution medium, communication channels are divided into:
4. What is telecommunications and computer telecommunications?Telecommunications(Greek tele - far away, and Lat. communicatio - communication) is the transmission and reception of any information (sound, image, data, text) over a distance through various electromagnetic systems (cable and fiber optic channels, radio channels and other wired and wireless channels connections).
telecommunications network- a system of technical means through which telecommunications are carried out.
Telecommunication networks include:
1. Computer networks (for data transmission)
2. Telephone networks (transmission voice information)
3. Radio networks (transmission of voice information - broadcast services)
4. TV networks(voice and image transmission - broadcast services)
Computer telecommunications- telecommunications, the terminal devices of which are computers.
The transfer of information from computer to computer is called synchronous communication, and through an intermediate computer that allows you to accumulate messages and transfer them to personal computers as requested by the user - asynchronous.
Computer telecommunications are beginning to take root in education. In higher education, they are used for the coordination of scientific research, the rapid exchange of information between project participants, distance learning, and consultations. In the system of school education - to increase the effectiveness of students' independent activities related to various types of creative work, including educational activities, based on the widespread use of research methods, free access to databases, exchange of information with partners both within the country and abroad.
5. What is the bandwidth of the information transmission channel?Bandwidth - metric characteristic, showing the ratio of the maximum number of passing units (information, objects, volume) per unit of time through a channel, system, node.
In computer science, the definition of bandwidth is usually applied to a communication channel and is defined the maximum number transmitted/received information per unit of time.
Bandwidth is one of the most important factors from the user's point of view. It is estimated by the amount of data that the network, in the limit, can transfer per unit of time from one device connected to it to another.
The speed of information transfer depends largely on the speed of its creation (source performance), encoding and decoding methods. The highest possible information transfer rate in a given channel is called its bandwidth. The channel capacity, by definition, is the information transfer rate when using the “best” (optimal) source, encoder and decoder for a given channel, therefore it characterizes only the channel.
Information transmission over a channel with decisive feedback
1.2.1 Methods for transmitting information over communication channels
Transfer of information with repetition (accumulation). This transmission method is used to improve reliability in the absence of a reverse channel, although there are no fundamental restrictions on its use even in the presence of feedback. This method is sometimes classified as cumulative message reception. The essence of the method lies in the transmission of the same message several times, storing the received messages, comparing them element by element and compiling a message, including the elements selected "by the majority". Suppose that the same codeword 1010101 is transmitted three times. In all three transmissions, it was interfered with and distorted:
The receiver bit by bit compares the three received symbols and puts down those symbols (under the line), the number of which prevails in this bit.
There is another method of transferring information with accumulation, in which not a character-by-character comparison is made, but a comparison of the entire combination as a whole. This method is easier to implement but produces poorer results.
Thus, the high noise immunity of the method of transmitting information with repetition (accumulation) is based on the fact that the signal and interference in the channel do not depend on each other and change according to different laws (the signal is periodic, and the interference is random), therefore, the repeating combination in each transmission, as the rule will be distorted in different ways. As a result, at the reception, the accumulation, that is, the summation of the signal, increases in proportion to the number of repetitions, while the sum of the interference increases according to a different law. If we assume that the interference and the signal are independent, then the mean squares are summed and the mean square of the sum increases in proportion to the first degree. Therefore, for n repetitions, the signal-to-noise ratio increases by a factor of n, and this occurs without increasing the signal strength. However, this is achieved at the cost of increased hardware complexity and increased transmission time or bandwidth if the signal is transmitted at multiple frequencies simultaneously in time. In addition, with dependent errors and bursts of errors, the noise immunity of the system decreases.
Transfer of information with feedback. The noise immunity of the transmission without feedback (FBOS) is provided in the following ways: error-correcting coding, transmission with repetition, simultaneous transmission through several parallel channels. In PBOS, error-correcting codes are usually used, which is associated with high redundancy and complexity of the equipment. Feedback transmission (FC) largely eliminates these shortcomings, since it allows the use of less noise-resistant codes, which, as a rule, have less redundancy. In particular, codes with error detection can be used. The advantage of the reverse channel is also the ability to control the health of the object receiving information.
With PIC, the concept of a direct channel is introduced, i.e. channel from the transmitter to the receiver, for example, a command signal is transmitted from the control point (CP) to the controlled point (CP). In this case, the reverse channel will be the transmission of a message from the CP to the CP about the acceptance of the command signal, and both the message that the signal was received at the input of the CP (in this case, only the passage of the signal through the communication channel) and information about the complete execution of the command. Feedback is also possible, giving information about the phased passage of the command signal along the receive path.
Consider certain types feedback transfers.
Transfer with information feedback (IOS). If the message is transmitted in the form of a non-interference code, then in the encoder given code can be converted to anti-jamming. However, since this is usually not necessary, the encoder is a register for converting a simple parallel code into a serial one. Simultaneously with the transmission direct channel the message is stored in the storage on the transmitter (Fig. 1.1a). At the controlled point, the received message is decoded and also stored in the drive. However, the message is not immediately transmitted to the recipient: first, it arrives through the reverse channel to the control point. In the PU comparison scheme, a comparison is made received message with transferred. If the messages match, then a “Confirmation” signal is generated and subsequent messages are transmitted (sometimes, before sending a subsequent message to the CP, a “Confirmation” signal is first sent that the previous message was received correctly and information can be transmitted from the drive to the recipient). If the messages do not match, which indicates an error, the "Erase" signal is generated. This signal locks the key to stop the transmission of the next message and is sent to the CP to destroy the message recorded in the drive. After that, the PU retransmits the message recorded in the drive.
Fig.1.1a. A method of transmitting information from the IOS.
In systems with IOS, the leading role belongs to the transmitting part, since it determines the presence of an error, the receiver only informs the transmitter about what message it has received. Available various options transfers from IOS. So, there are systems with IOS in which the transmission of signals occurs continuously and stops only when an error is detected: the transmitter sends the “Erase” signal and repeats the transmission. Systems with IOS, in which all information transmitted to the CP is transmitted over the reverse channel, are called systems with relay feedback. In some systems with IOS, not all information is transmitted, but only some characteristic information about it (receipts). For example, information is transmitted over the forward channel, and control characters are transmitted over the reverse channel, which will be compared at the transmitter with pre-recorded control characters. There is a variant in which, after checking the message received on the reverse channel and detecting an error, the transmitter can either repeat it (doubling the message) or send Additional information required for correction (corrective information). The number of repetitions can be limited or unlimited.
The reverse channel is used to determine if retransmission of information is necessary. In systems with IOS, an increase in the reliability of transmission is achieved by repeating information only in the presence of an error, while in systems without feedback (in case of accumulation transmission), repetition is carried out regardless of message distortion. Therefore, in systems with IOS, the redundancy of information is much less than in systems with PBOS: it is minimal in the absence of distortions and increases with errors. In systems with IOS, the quality of the reverse channel should not be worse quality direct to avoid distortion that can increase the number of repetitions.
Decisive feedback transmission (ROS). The message transmitted from the transmitter over the direct channel is received at the receiver (Fig. 1.1b), where it is stored and checked in the decoding device (decoder). If there are no errors, then the message is sent from the storage device to the recipient of information, and a signal is sent to the transmitter through the reverse channel to continue further transmission (continuation signal). If an error is detected, the decoder generates a signal that erases the information in the drive. The recipient does not receive a message, and through the reverse channel a signal is sent to the transmitter to ask again or repeat the transmission (repeat or repeat signal). At the transmitter, the repetition signal (sometimes called the decisive signal) is isolated by the decisive signal receiver, and the switching device disconnects the encoder input from the information source and connects it to the storage device, which allows repeating the transmitted message. The repetition of the message may occur several times before it is correctly received.
Fig.1.1b. The method of transmitting information from ROS.
When transmitting with ROS, the error is determined by the receiver. For this transmitted message must be encoded with a mandatory anti-jamming code, which allows the receiver to distinguish the allowed combination (message) from the unallowed ones. This means that the transmission with the ROS is carried out with redundancy. Transmission reliability in POC systems is determined by the choice of code and the protection of the repeat and continue decision signals. The latter does not present any particular difficulties, since these signals carry one binary unit of information and can be transmitted in a fairly error-correcting code.
Systems with ROS, or systems with a repeat request, are divided into systems with the expectation of a decisive signal and systems with continuous transmission of information.
In systems with waiting, the transmission of a new codeword or the repetition of the transmitted one occurs only after the transmitter receives a request signal.
In systems with continuous transmission, information is continuously transmitted without waiting for a request signal. The transmission speed is higher than in systems with waiting. However, after an error is detected, a repeat request signal is sent over the reverse channel, and during the time it arrives at the transmitter, some new message will already be transmitted from the latter. Therefore, systems with continuous transmission must be complicated by appropriate blocking of the receiver so that it does not receive information after an error is detected.
To compare the efficiency of an open-loop system using a Hamming code with one error correction, and a system with a POC using a simple code, the concept of an efficiency factor is introduced. This coefficient takes into account the reduction in the probability of erroneous reception and the cost of achieving it, the gain in error protection (in the case of the use of these codes), the relative reduction in transmission rate and circuit redundancy associated with the use of different codes. The final comparison showed that, in contrast to the system without feedback using a complex code, the system with POC gives a gain of 5.1 times. The high efficiency of systems with ROS ensured their widespread use.
A comparative analysis of the reliability of the transmission of systems with IOS and ROS showed that:
1) systems with IOS and ROS provide the same transmission reliability with the same total energy consumption of signals in the direct and return channels provided that these channels are symmetrical and have the same level of interference;
2) systems with IOS provide a higher transmission reliability than systems with ROS with relatively weak interference in the reverse channel, in contrast to the direct one. In the absence of interference in the reverse channel, systems with IOS provide error-free transmission of messages over the main channel;
3) when strong interference in the reverse channel, systems with ROS provide higher reliability;
4) with bursts of errors in the forward and reverse channels, systems with IOS provide higher reliability.
1.1 Acoustic information Protected speech (acoustic) information includes information that is the subject of property and is subject to protection in accordance with the requirements of legal documents or the requirements ...
Protection of acoustic (speech) information from leakage through technical channels
Protection of acoustic (speech) information from leakage through technical channels
Spatial noise generators The GROM-ZI-4 noise generator is designed to protect premises from information leakage and personal computers and local computer networks PC based...
Information security methods
Information security methods in telecommunication networks
A threat is usually identified either with the nature (type, method) of a destabilizing effect on information, or with the consequences (results) of such an effect. However, such terms can have many interpretations ...
Collection and processing methods digital signals
Data transmission - the physical transfer of data (digital bit stream) in the form of signals from point to point or from point to several points by means of telecommunications over a data channel, usually ...
Modeling the object of protection
3.1 Leakage of information through building construction and engineering systems To ensure the protection of the premises from this threat, it can be used as a method of passive protection (sound-absorbing materials) ...
Determination of the composition of the information transmission system
The signal at the output of the PTI equipment is, as a rule, a pulse-coded signal, the frequency spectrum of which is general case endless...
Organization of work on the construction of a fiber-optic communication line (FOCL)
The possibility of transmitting information over fiber-optic lines appeared due to the transposition of the quantum theory of light to its propagation in transparent homogeneous media...
3.1 Transmission capability analysis confidential information through quantum communication channels In the transition from signals, where information is encoded by pulses containing thousands of photons, to signals, where the average number of photons ...
Information transfer via quantum communication channels
An example of an error correction protocol is an error correction method in which a block of data to be negotiated between users is considered as information block some code...
Design and software implementation integrated system turnouts
A communication channel is a communication path that begins with information source, goes through all stages of coding and modulation, transmitter, physical channel...
Designing a backbone fiber-optic transmission system with increased bandwidth
The development of telecommunications is accelerating. Widespread development of modern digital technologies data transmissions, which include ATM, frame relay, IP, ISDN, PCM, PDH, SDH and WDM. Moreover, such technologies as ATM, ISDN, PCM, PDH...
Calculation of the reliability of the atmospheric optical communication line
This chapter discusses the technology of laser communication network, as well as its advantages, such as economy; low operating costs; high throughput and quality digital communication...
Communication channel is a set of technical means and a physical medium capable of transmitting sent signals, which ensures the transmission of messages from the source of information to the recipient.
Channels are usually divided into continuous and discrete.
In the most general case, any discrete channel includes a continuous channel as an integral part. If the influence of interfering factors on the transmission of messages in a channel can be neglected, then such an idealized channel is called channel without interference . In such a channel, each message at the input uniquely corresponded to a specific message at the output, and vice versa. If the influence of interference in a channel cannot be neglected, then when analyzing the features of messages transmitted over such a channel, models characterizing the operation of the channel in the presence of interference.
Under channel model refers to a mathematical description of a channel that allows one to calculate or evaluate its characteristics, on the basis of which methods for constructing communication systems are studied without conducting experimental studies.
The channel in which the probabilities of identifying the first signal with the second and the second with the first are the same is called symmetrical .
A channel, the alphabet of signals at the input of which differs from the alphabet of signals at its output, is called channel with erasure.
The channel for transmitting a message from the source to the recipient, supplemented by a reverse channel, serves to increase the reliability of the transmission is called feedback channel.
A communication channel is considered to be given if the data on the message at its input are known, as well as the restrictions that are imposed on the input messages by the physical characteristics of the channels.
To characterize communication channels, two concepts of transmission speed are used:
1 – technical transmission speed, which is characterized by the number of elementary signals transmitted over the communication channel per unit time, it depends on the properties of the communication lines and on the speed of the channel equipment:
2 – information speed, which is determined by the average amount of information transmitted over the communication channel per unit of time:
Channel capacity is the maximum rate of information transfer over this channel, achieved with the most advanced methods of transmission and reception.
Lecture #8
Coordination of the physical characteristics of the communication channel and signal
Each specific communication channel has physical parameters that determine the possibility of transmitting certain signals over this channel. Regardless of the specific type and purpose, each channel can be characterized by three main parameters:
T K – channel access time [s];
F K – channel bandwidth [Hz];
НК - permissible excess of the signal over noise in the channel.
Based on these characteristics, an integral characteristic is used - channel volume.
Consider the following cases:
but) 
To assess the possibility of transmitting a given signal over a specific channel, it is necessary to correlate the characteristics of the channel with the corresponding characteristics of the signal:
T C – signal duration [s];
F C is the frequency band (spectrum width) of the signal [Hz];
H C is the level of signal excess over interference.
Then we can introduce the concept signal volume .
The transfer of information occurs from the source to the recipient (receiver) of information. source information can be anything: any object or phenomenon of living or inanimate nature. The process of information transfer takes place in some material environment that separates the source and recipient of information, which is called channel transfer of information. Information is transmitted through a channel in the form of a certain sequence of signals, symbols, signs, which are called message. Recipient information is an object that receives a message, as a result of which certain changes in its state occur. All of the above is shown schematically in the figure.
Transfer of information
A person receives information from everything that surrounds him, through the senses: hearing, sight, smell, touch, taste. A person receives the greatest amount of information through hearing and sight. Perceived by ear audio messages- acoustic signals in a continuous medium (most often - in the air). Vision perceives light signals, carrying the image of objects.
Not every message is informative for a person. For example, a message in an incomprehensible language, although transmitted to a person, does not contain information for him and cannot cause adequate changes in his state.
An information channel can either be of a natural nature (atmospheric air through which sound waves are transmitted, sunlight reflected from observed objects), or be artificially created. IN last case we are talking about technical means of communication.
Technical information transmission systems
The first technical means of transmitting information over a distance was the telegraph, invented in 1837 by the American Samuel Morse. In 1876, the American A. Bell invents the telephone. Based on the discovery by the German physicist Heinrich Hertz electromagnetic waves(1886), A.S. Popov in Russia in 1895 and almost simultaneously with him in 1896 G. Marconi in Italy, radio was invented. Television and the Internet appeared in the twentieth century.
All of the above technical ways information communication are based on the transmission of a physical (electrical or electromagnetic) signal over a distance and are subject to certain general laws. The study of these laws is communication theory that emerged in the 1920s. Mathematical apparatus of communication theory - mathematical theory of communication, developed by the American scientist Claude Shannon.
Claude Elwood Shannon (1916–2001), USA
Claude Shannon proposed a model for the process of transmitting information through technical communication channels, represented by a diagram.
Technical information transmission system
Encoding here means any transformation of information coming from a source into a form suitable for its transmission over a communication channel. Decoding - inverse transformation of the signal sequence.
The operation of such a scheme can be explained by the familiar process of talking on the phone. The source of information is talking man. An encoder is a handset microphone that converts sound waves (speech) into electrical signals. The communication channel is telephone network(wires, switches of telephone nodes through which the signal passes). The decoding device is a handset (headphone) of the listening person - the receiver of information. Here come electrical signal turns into sound.
Modern computer systems transmission of information - computer networks operate on the same principle. There is an encoding process that converts the binary computer code in physical signal of the type that is transmitted over the communication channel. The decoding is inverse transformation transmitted signal into computer code. For example, when using telephone lines in computer networks The functions of encoding and decoding are performed by a device called a modem.
Channel capacity and information transfer rate
Developers technical systems transmission of information, two interrelated tasks have to be solved: how to ensure top speed transmission of information and how to reduce the loss of information during transmission. Claude Shannon was the first scientist who took on the solution of these problems and created a new science for that time - information theory.
K.Shannon determined the method of measuring the amount of information transmitted over communication channels. They introduced the concept channel bandwidth,as the maximum possible information transfer rate. This speed is measured in bits per second (as well as kilobits per second, megabits per second).
The throughput of a communication channel depends on its technical implementation. For example, computer networks use the following means of communication:
telephone lines,
Electrical cable connection,
fiber optic cabling,
Radio communication.
Throughput of telephone lines - tens, hundreds of Kbps; the throughput of fiber optic lines and radio communication lines is measured in tens and hundreds of Mbps.
Noise, noise protection
The term "noise" refers to different kind interference that distorts transmitted signal and leading to loss of information. Such interference primarily arises for technical reasons: poor quality communication lines, insecurity from each other of various information flows transmitted over the same channels. Sometimes, while talking on the phone, we hear noise, crackling, which make it difficult to understand the interlocutor, or the conversation of completely different people is superimposed on our conversation.
The presence of noise leads to loss transmitted information. In such cases noise protection is necessary.
First of all, technical methods are used to protect communication channels from the effects of noise. For example, using shielded cable instead of bare wire; the use of various kinds of filters that separate the useful signal from noise, etc.
Claude Shannon developed coding theory, which gives methods for dealing with noise. One of the important ideas of this theory is that the code transmitted over the communication line must be redundant. Due to this, the loss of some part of the information during transmission can be compensated. For example, if you are hard to hear when talking on the phone, then by repeating each word twice, you have a better chance that the interlocutor will understand you correctly.
However, you can not make the redundancy too large. This will lead to delays and higher communication costs. Coding theory allows you to get a code that will be optimal. In this case, the redundancy of the transmitted information will be the minimum possible, and the reliability of the received information will be the maximum.
IN modern systems In digital communication, the following technique is often used to combat the loss of information during transmission. The whole message is divided into portions - packages. For each package is calculated check sum(sum binary digits) that is sent with this packet. The checksum is recalculated at the receiving end. received package and, if it does not match the original amount, the transfer this package repeats. This will continue until the initial and final checksums won't match.
Considering the transfer of information in propaedeutic and basic courses Informatics, first of all, this topic should be discussed from the position of a person as a recipient of information. The ability to receive information from the surrounding world - essential condition human existence. The human sense organs are information channels of the human body, which connects a person with external environment. On this basis, information is divided into visual, auditory, olfactory, tactile, and gustatory. The rationale for the fact that taste, smell and touch carry information to a person is as follows: we remember the smells of familiar objects, the taste of familiar food, we recognize familiar objects by touch. And the content of our memory is stored information.
You should tell the students that in the animal world informational role sense organs are different from human. important information function performs sense of smell for animals. The heightened sense of smell of service dogs is used law enforcement to search for criminals, detect drugs, etc. The visual and sound perception of animals differs from that of humans. For example, bats are known to hear ultrasound, and cats are known to see in the dark (from a human perspective).
Within the framework of this topic, students should be able to lead concrete examples the process of information transfer, to determine for these examples the source, receiver of information, used information transmission channels.
When studying computer science in high school, students should be introduced to the basic provisions of the technical theory of communication: the concepts of coding, decoding, information transfer rate, channel capacity, noise, noise protection. These issues can be considered within the framework of the topic “Technical means of computer networks”.
A communication channel is a set of technical means for transmitting messages from one point in space to another. From the point of view of information theory, the physical structure of the channel is not essential. The message source(IS) has an output character alphabet A={but i },i=1.. n- the amount of information per symbol of the source on average:
where p i, - probability of occurrence of a symbol a i, at the source output, the source symbols are considered independent. The communication channel has a character alphabet B=( b j },j=1.. m, average amount of information in one channel symbol
where q j - probability of occurrence of a symbol b i , in the channel.
The technical characteristics of the communication channel are:
technical performance of the source A - the average number of characters produced by the source per unit of time;
technical bandwidth of the communication channel B - the average number of symbols transmitted over the channel per unit of time.
The information characteristic of the source is the information productivity. By definition, information productivity is the average amount of information produced by a source per unit of time.
In a channel without interference, the information characteristics are:
1) the rate of information transfer over the channel 
2) channel capacity
where ( P) - the set of all possible probability distributions of alphabet symbols IN channel. Taking into account the properties of entropy
C K = B . log 2m.
In a noisy channel, in the general case, the input and output alphabets do not coincide. Let be
B BX \u003d X \u003d (x 1, x 2, ..., x n);
B OUT =Y=(y 1 ,y 2 ,…,y m ).
If the symbol sent at the input of the channel X to recognized at the receiver as y i And i K, an error occurred during transmission. Channel properties are described by a matrix of transition probabilities (probability of receiving a symbol at i , provided that it is sent X k):
|| P(yi|xk) ||, k=1..n, i=1..m.
Fair ratio: 
Average amount of information per input channel symbol:
p i =p(x i )
.
Average amount of information per channel output symbol:
Information carried by the channel output about the input:
I(Y,X)=H(X)-H Y (X)=H(Y)-H X (Y).
Here well(X) - the conditional entropy of the channel's input symbol while observing the output symbol (channel unreliability), H X (Y) - conditional entropy of the output symbol of the channel when observing the input symbols (noise entropy).
Information transfer rate over a noisy channel:
dI(B)/dt= B I(X, Y).
Bandwidth of a noisy channel:
where ( R) - the set of all possible probability distributions of the input alphabet of channel symbols.
Consider an example
H 
find the capacity of a binary symmetric channel (a channel with two-symbol input and output alphabets) and equal error probabilities (Fig. 1), if the a priori probabilities of occurrence of input symbols: P(x 1
)=P 1
=P, P(x 2
)=P 2
=1-P.
Solution. According to the channel model, the conditional probabilities
P(y 1 | x 2 ) = P(y 2 | x 1 ) = P i ,
P(y 1 | x 1 ) = P(y 2 | x 2 ) = 1-P i .
Channel capacity - C K = B . max(H(Y)-H(X|Y)). Let's find the entropy of the noise:
According to the multiplication theorem: P(y j x i)=P(x i)P(y j |x i), Consequently,
P(x 1 y 1 )=P(1-P i), P(x 2 y 1 )=(1- P)P i ,P(x 1 y 2 )=PP i ,P(x 2 y 2 )=(1-P)(1-P i).
Substituting into the formula, we get:
In this way, H( Y| X ) does not depend on the distribution of the input alphabet, therefore:
We define the entropy of the output:
Probabilities P(y 1 ) And P(y 2 ) we get as follows:
P(y 1 )=P(y 1 x 1 )+P(y 1 x 2 )=P(1-P i)+(1-P i)P i , P(y2)=P(y 2 x 1 )+P(y 2 x 2 )=PP i +(1-P)(1-P i).
By varying P, we make sure that the maximum value H(Y) equal to 1 is obtained with equiprobable input symbols P(y 1 ) And P(y 2 ). Consequently,
A task. Find the capacity of a channel with three-character input and output alphabets ( x 1 ,x 2 ,x 3 And y 1 ,y 2 ,y 3 respectively). The intensity of the appearance of symbols at the channel input k = V. 10 characters/s.
Symbol appearance probabilities:
,
,
.
Probabilities of character transmission through a communication channel:
,
,,
,
,,
,
,.
4. ENCODING INFORMATION
4.1. General information A code is:
A rule describing the mapping from one character set to another character set or to a set of unsigned words;
The set of images resulting from such a mapping.
In technical codes, letters, numbers, and other characters are almost always encoded in binary sequences called binary code words. Many codes have words of the same length (uniform codes).
The choice of codes for encoding specific types of messages is determined by many factors:
Ease of getting original messages from the source;
Speed of message transmission through the communication channel;
The amount of memory required for a day of storing messages;
Ease of data processing;
Convenience of decoding messages by the receiver.
Encoded messages are transmitted over communication channels, stored in memory, processed by the processor. The volume of encoded data is large, And therefore, in many cases it is important to provide a data encoding rate: ", which is characterized by the minimum length of the resulting messages. This is a data compression problem. There are two approaches to data compression:
Compression based on the analysis of the statistical properties of encoded messages.
Compression based on the statistical properties of the data is also called the theory of economical or efficient coding. Economy coding is based on the use of codes with a variable codeword length, for example, the Shannon-Fano code, the Huffman code /31. The idea of using variable length codes for data compression is to match messages with a higher probability of occurrence to code combinations of smaller length and, conversely, encode messages with a low probability of occurrence in words of greater length. Average length code word is determined by s.o.:
where /, is the length of the code word for encoding the i -th message; p t - probability of occurrence of the i -th message.
4.2. Tasks
4.2.1. From Table 4, select the days of subsequent coding, the initial alphabet containing 10 characters, starting with N-ro (N- the student's serial number in the group journal). Normalize the probabilities of symbols.
4.2.2. Normalize the one selected in Section 4.2.1. initial alphabet by uniform binary code, Shannon-Fano code, Huffman code. For each coding option, calculate the minimum, maximum, average value of the length of the code word. Analyze results.
4.2.3. Complete task 4.2.2. for ternary code.
Table 4
4.3. Instructions for performing individual tasks For task 4.2.1. The normalization of probabilities is carried out according to the formula:
/W-HO /*pk " JC=AT
where Pi- the probabilities of occurrence of symbols given in Table 4.
To task 4.2.2. The rules for constructing binary codes are set out in /4,6/.
To task 4.2.3. When constructing a ternary code, words written in the ternary number system are taken as code words. The optimal ternary code is built using the Huffman procedure (using the Shannon-Fano procedure, a suboptimal code is built). In this case, the alphabet is divided into three groups, the first group is assigned "O", the second - "1", the third - "2".
